Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Table of handwritten notes

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            <s xml:id="echoid-s8719" xml:space="preserve">
              <pb o="347" file="0367" n="367" rhead="LIBER IV."/>
            CI, & </s>
            <s xml:id="echoid-s8720" xml:space="preserve">ſic eſſe quodlibet ſolidum ſimilare genitũ ex parabola, FCH,
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            ad ſibi ſimilare genitum ex parabola OCM, iuxta communem re-
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            gulam, FH, ſiue CG, ſit axis, ſiue tantum diameter, quod iuxta an-
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            tecedentis explicationem facilè intelligi poteſt.</s>
            <s xml:id="echoid-s8721" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div834" type="section" level="1" n="493">
          <head xml:id="echoid-head513" xml:space="preserve">COROLLARIVM III.</head>
          <p>
            <s xml:id="echoid-s8722" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8723" xml:space="preserve">23. </s>
            <s xml:id="echoid-s8724" xml:space="preserve">aſſumpta figura Prop. </s>
            <s xml:id="echoid-s8725" xml:space="preserve">12. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">ſcilicet parabola, BNH,
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            parallelogrammis, PH, AG, & </s>
            <s xml:id="echoid-s8727" xml:space="preserve">triangulo, BRH, reuoluatur pa-
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              <figure xlink:label="fig-0367-01" xlink:href="fig-0367-01a" number="249">
                <image file="0367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0367-01"/>
              </figure>
            rabola, BNH, vt fiat noſſrum exem-
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            plum, circa axem, NO, & </s>
            <s xml:id="echoid-s8728" xml:space="preserve">inſimul, PH,
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            AG, & </s>
            <s xml:id="echoid-s8729" xml:space="preserve">triangulus, BRH, circa RO,
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            patebit ergo cylindrum ex, PO, ad
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            fruſtum conoidis ex, ABOR, in reuo-
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            lutione genitum, eſſe vt, ON, ad com-
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            poſitam ex, NR, & </s>
            <s xml:id="echoid-s8730" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">RO, ipſum ve-
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            rò ad idem dempto cylindro ex, AO,
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            .</s>
            <s xml:id="echoid-s8732" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8733" xml:space="preserve">AG, vt, NO, ad {1/2}. </s>
            <s xml:id="echoid-s8734" xml:space="preserve">RO, ex Corollario huic Propoſitioni ſubiecto,
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            hoc fruſtum tandem ad conum gentium ex triangulo, RBO, vt cõ-
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            poſita ex, ON, dupla, MR, & </s>
            <s xml:id="echoid-s8735" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8736" xml:space="preserve">RO, adipſam, NO; </s>
            <s xml:id="echoid-s8737" xml:space="preserve">& </s>
            <s xml:id="echoid-s8738" xml:space="preserve">vniuerſa-
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            liter quæcunque ſolida ſimilaria ex eiſdem figuris genitricibus geni-
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            ta, iuxta communem regulam, BH, eaſdem rationes habere, vt ſu-
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            pradicta ad inuicem comparata, ſiue, NO, ſit axis, ſiue tantum dia-
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            meter; </s>
            <s xml:id="echoid-s8739" xml:space="preserve">quod ex Propol. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">51. </s>
            <s xml:id="echoid-s8741" xml:space="preserve">clarè patet. </s>
            <s xml:id="echoid-s8742" xml:space="preserve">Intelligatur autem in ſe-
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            quentibus, licet ſemper aſſumatur axis, tamen pro ſolidis ſimilari-
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            bus etiam aſſu mptis diametris eadem ibi appoſita verificari.</s>
            <s xml:id="echoid-s8743" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div836" type="section" level="1" n="494">
          <head xml:id="echoid-head514" xml:space="preserve">COROLLARIVM IV.</head>
          <p>
            <s xml:id="echoid-s8744" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s8745" xml:space="preserve">26. </s>
            <s xml:id="echoid-s8746" xml:space="preserve">veluti oſtendimus in eiuſdem figura hic appoſita
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              <figure xlink:label="fig-0367-02" xlink:href="fig-0367-02a" number="250">
                <image file="0367-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0367-02"/>
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            omnia quadrata portionis, BSF,
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            ad rectangula ſub portione, BSF, & </s>
            <s xml:id="echoid-s8747" xml:space="preserve">
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            figura diſtantiarum, SEF, eſſe vt, BF,
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            ad FE, ſic oſtenſum fuiſſet (aſſumptis
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            vice quadratorum alijs figuris ſimili-
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            bus, & </s>
            <s xml:id="echoid-s8748" xml:space="preserve">vice rectangulorum, aſſumptis
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            alijs ſimilibus figuris eius generis, vt
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            veluti eſt vnum quoduis dictorum
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            omnium quadratorum ad rectãgulum adiacens lateri, à quo deſcri-
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            bitur, ita ſit figura ab eodem latere deſcripta vice quadrati ſumpta,
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            ad figuram deſcriptam eodem latere vice rectanguli ſumptam, </s>
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